Finding the angle of a falling person on a sphere

A sphere is on the ground, with the sphere having a radius R. A person (skier) is standing on top of the sphere. neglecting friction, find the angle at which the person will slide off the sphere if he moves from rest to a constant velocity of v.

The centripetal force is the force towards the center due to gravity and the normal... if the skier is moving along the sphere:

the net force towards the center = mv^2/r

component of gravity towards the center - normal force = mv^2/r

When the component of gravity towards the center becomes less than mv^2/r it is impossible for the skier to move along the sphere... force towards the center at this point cannot be mv^2/r because the normal force can't be negative...